
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Excited state linear response functions and
         two-photon transition moments between two excited states:
         \Sec{CCEXLR}}
\label{sec:ccexlr}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Coupled Cluster!linear response}
\index{linear response!excited states, CC}
\index{response!linear, CC}
\index{excited state!linear response, CC}
\index{excited state!two-photon, CC}
\index{polarizability!frequency-dependent, CC}
\index{two-photon!transition moments betweenexcited states, CC}
\index{second residues of cubic response functions}
\index{second-order properties!excited states, CC}
\index{properties!second-order, CC}

In the \Sec{CCEXLR} section input that is specific for 
double residues of coupled cluster cubic response functions 
is read in.
Results obtained using this functionality should cite
Ref.~\cite{Haettig:EXCITED,Haettig:EXLR}. 
This section includes:
\begin{itemize}
\item frequency-dependent second-order properties of excited states
      $$ \alpha^{(i)}_{AB}(\omega) = 
         -\langle\langle A; B\rangle\rangle^{(i)}_\omega $$
      where $A$ and $B$ can be any of the one-electron operators
      for which integrals  are available in the \Sec{*INTEGRALS}
      input part.
\item two-photon transition moments between excited states.
\end{itemize}
Double residues of coupled cluster cubic response functions are
implemented for the models CCS, CC2, CCSD, and CC3.
%Publications that report results obtained with double residues
%of CC cubic response functions should cite Ref.\ \cite{Haettig:EXLR}.

\begin{center}
\fbox{
\parbox[h][\height][l]{12cm}{
\small
\noindent
{\bf Reference literature:}
\begin{list}{}{}
\item C.~H\"{a}ttig, and P.~J{\o}rgensen \newblock {\em J.~Chem.~Phys.}, {\bf 109},\hspace{0.25em}4745, (1998).
\item C.~H\"{a}ttig, O.~Christiansen, S.~Coriani, and P.~J{\o}rgensen \newblock {\em J.~Chem.~Phys.}, {\bf 109},\hspace{0.25em}9237, (1998).
\end{list}
}}
\end{center}

\begin{description}
\item[\Key{ALLSTA}] 
Calculate excited-state polarizabilities for all excited states.
 
\item[\Key{DIPOLE}] 
Evaluate all symmetry-allowed elements of the dipole--dipole tensor
of the double residues of the cubic response function 
(a maximum of six components for second-order properties, and a
 maximum of nine for two-photon transition moments).
 
\item[\Key{FREQ}]  \verb| |\newline
%  or \Key{FREQUE}
\verb|READ (LUCMD,*) MFREQ|\newline
\verb|READ (LUCMD,*) (BEXLRFR(IDX),IDX=NEXLRFR+1,NEXLRFR+MFREQ)|

Frequency input for $\alpha^{(i)}_{AB}(\omega)$.
 
\item[\Key{HALFFR}] 
Use half the excitation energy as frequency argument for two-photon
transition moments.
Note that the \Key{HALFFR} keyword is incompatible with a 
user-specified list of frequencies. \\
For excited-state second-order properties the \Key{HALFFR} keyword is
equivalent to the \Key{STATIC} keyword.
 
\item[\Key{OPERAT}] \verb| |\newline
\verb|READ (LUCMD,'(2A8)') LABELA, LABELB|\newline
\verb|DO WHILE (LABELA(1:1).NE.'.' .AND. LABELA(1:1).NE.'*')|\newline
\verb|  READ (LUCMD,'(2A8)') LABELA, LABELB|\newline
\verb|END DO|

Read pairs of operator labels, using exactly 8 characters for each. 
This means that if you should want e.g LABELA='XXROTSTR' and LABELB='YYROTSTR'
you must enter\newline
\verb|XXROTSTRYYROTSTR|

For each of these operator pairs, the double residues of the cubic response
function will be evaluated at all frequencies.
Operator pairs which do not correspond to symmetry-allowed
combinations will be ignored during the calculation.
 
\item[\Key{PRINT}] \verb| |\newline
\verb|READ (LUCMD,*) IPRINT|

Set print parameter for the \Sec{CCEXLR} section.
 
\item[\Key{SELSTA}] \verb| |\newline
\verb|READ (LUCMD,'(A80)') LABHELP|\newline
\verb|DO WHILE(LABHELP(1:1).NE.'.' .AND. LABHELP(1:1).NE.'*')|\newline
\verb|  READ(LUCMD,*) ISYMS(1), IDXS(1), ISYMS(2), IDXS(2)|\newline
\verb|END DO|

Read symmetry and index of the initial state and the final state.
If initial and final state coincide one obtains excited state
second-order properties (or, more precisely, the difference of the excited state second-order property relative to the ground-state property), if the two excited states are different one obtains the
two-photon transition moments between the two excited states.
 
\item[\Key{STATIC}] 
Add $\omega = 0$ to the frequency list.
 
\item[\Key{USELEF}] 
Use left excited-state response vectors instead of the right excited-state response vectors (default is to use the right excited-state
response vectors).
 
\end{description}
